Q. 134.6( 13 Votes )

In each of

Answer :

Foci ( 4, 0), the latus rectum is of length 12


Here, the foci are on x-axis.


Thus,


The equation of the hyperbola is of the form


Since, the foci are ( 4, 0), c = 4


Length of latus rectum = 12



b2 = 6a


We know that, a2 + b2 = c2


a2 + 6a = 16


a2 + 6a -16 = 0


a2 + 8a – 2a - 16 = 0


(a +8)(a -2) = 0


A = -8, 2


Since, a is non – negative, a = 2


Thus, b2 = 6a = 6 × 2 = 12


Hence, the equation of the hyperbola is


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